Ta có : \(\frac{\sqrt{3}-3}{\sqrt{2-\sqrt{3}}+2\sqrt{2}}+\frac{\sqrt{3}+3}{\sqrt{2+\sqrt{3}}-2\sqrt{2}}\)
= \(\frac{\sqrt{2}\left(\sqrt{3}-3\right)}{\sqrt{4-2\sqrt{3}}+4}+\frac{\sqrt{2}\left(\sqrt{3}+3\right)}{\sqrt{4+2\sqrt{3}}-4}\)\(=\frac{\sqrt{2}\left(\sqrt{3}-3\right)}{\sqrt{3-2\sqrt{3}+1}+4}+\frac{\sqrt{2}\left(\sqrt{3}+3\right)}{\sqrt{3+2\sqrt{3}+1}-4}\)
\(=\frac{\sqrt{2}\left(\sqrt{3}-3\right)}{\sqrt{\left(\sqrt{3}-1\right)^2}+4}+\frac{\sqrt{2}\left(\sqrt{3}+3\right)}{\sqrt{\left(\sqrt{3}+1\right)^2}-4}\)\(=\frac{\sqrt{2}\left(\sqrt{3}-3\right)}{\sqrt{3}+3}+\frac{\sqrt{2}\left(\sqrt{3}+3\right)}{\sqrt{3}-3}\)
\(=\frac{\sqrt{2}\left(\sqrt{3}-3\right)^2}{\left(\sqrt{3}+3\right)\left(\sqrt{3}-3\right)}+\frac{\sqrt{2}\left(\sqrt{3}+3\right)^2}{\left(\sqrt{3}-3\right)\left(\sqrt{3}+3\right)}\)\(=\frac{\sqrt{2}\left(3-6\sqrt{3}+9\right)}{-6}+\frac{\sqrt{2}\left(3+6\sqrt{3}+9\right)}{-6}\)
\(=\frac{3\sqrt{2}-6\sqrt{6}+9\sqrt{2}+3\sqrt{2}+6\sqrt{6}+9\sqrt{2}}{-6}\)\(=\frac{24\sqrt{2}}{-6}=-4\sqrt{2}\)
